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\log_{10}\left(\frac{0.0001}{10^{8}}\right)
Cancel out 10^{7} in both numerator and denominator.
\log_{10}\left(\frac{0.0001}{100000000}\right)
Calculate 10 to the power of 8 and get 100000000.
\log_{10}\left(\frac{1}{1000000000000}\right)
Expand \frac{0.0001}{100000000} by multiplying both numerator and the denominator by 10000.
-12
The base 10 logarithm of \frac{1}{1000000000000} is -12.